Rig does not move the mesh
Try Joining the Meshes Before Parenting to Rigify

The reason why parenting may not have worked is because your mesh is in multiple parts. 

Joining the meshes together before parenting to the rig should fix your problem.

For your cyclops file, here's what I did:

Select one mesh, press 'SHIFT+G' choose 'type'

Join your meshes. 'CTRL+J'

Press 'Tab' to go to edit mode

Remove doubles. press 'A' until everything is selected > 'W' > 'remove doubles'

Delete all vertex groups from the vertex groups panel

Delete all armature modifiers from the modifier in modifier panel

Select your armature and set it to pose mode. CTRL + tab

Select the mesh, then the armature, press CTRL+P, choose 'automatic weights'

Now your mesh should deform when you pose the armature in pose mode.

If and when you edit the weight values for each bone/vertex group, the deformation bones are on layer 29 of the bone layers ( not the regular layers )

Good Luck

Btw, cool model, where is it from?

Here's a link to your working file:


Here's a general video about setting up rigify in general :

https://www.youtube.com/watch?v=dYiAd_08-0k&amp;t=140s